I've read that the logistic map can be used to generate random numbers for K=4 (chaos regime)

x_n+1 = K*x_n*(1-x_n)

The logistic map for K=4 is isomorphic to the tent map. However, orbits in the tent map are non-periodic only for irrational initial values (x_0). For rational x_0, the tent map generates always periodic orbits.

My question is, is this the case also for the logistic map with K=4?. In that case, all orbits would be periodic, because computers can only handle rational numbers, and therefore x_0 must be a rational number.

well since computers are finite state machines then yes it'll have to repeat therefore periodic. furthermore since this 'random' number generator generates its value from a constant and with a formula its pseudo random, therefore by definition again its periodic it might be a long period but it is periodic. if you plug in the same seed you'll get the same output stream.

well since computers are finite state machines then yes it'll have to repeat therefore periodic. furthermore since this 'random' number generator generates its value from a constant and with a formula its pseudo random, therefore by definition again its periodic it might be a long period but it is periodic. if you plug in the same seed you'll get the same output stream.

Indeed, it's pseudo-random, but that does not mean it is periodic. For instance, the sequence 0.1, 0.01, 0.001, ... it's definitely not random, but it's not periodic either.